Average Error: 2.0 → 0.1
Time: 29.7s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 3.442415825498342 \cdot 10^{+150}:\\ \;\;\;\;\frac{a \cdot {k}^{m}}{k \cdot k + \left(k \cdot 10 + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{k} \cdot \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} + \left(\frac{99}{k \cdot k} \cdot \left(\frac{a}{k} \cdot \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k}\right) - \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)} \cdot \left(10 \cdot a\right)}{\left(k \cdot k\right) \cdot k}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 3.442415825498342 \cdot 10^{+150}:\\
\;\;\;\;\frac{a \cdot {k}^{m}}{k \cdot k + \left(k \cdot 10 + 1\right)}\\

\mathbf{else}:\\
\;\;\;\;\frac{a}{k} \cdot \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} + \left(\frac{99}{k \cdot k} \cdot \left(\frac{a}{k} \cdot \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k}\right) - \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)} \cdot \left(10 \cdot a\right)}{\left(k \cdot k\right) \cdot k}\right)\\

\end{array}
double f(double a, double k, double m) {
        double r3623828 = a;
        double r3623829 = k;
        double r3623830 = m;
        double r3623831 = pow(r3623829, r3623830);
        double r3623832 = r3623828 * r3623831;
        double r3623833 = 1.0;
        double r3623834 = 10.0;
        double r3623835 = r3623834 * r3623829;
        double r3623836 = r3623833 + r3623835;
        double r3623837 = r3623829 * r3623829;
        double r3623838 = r3623836 + r3623837;
        double r3623839 = r3623832 / r3623838;
        return r3623839;
}
↓
double f(double a, double k, double m) {
        double r3623840 = k;
        double r3623841 = 3.442415825498342e+150;
        bool r3623842 = r3623840 <= r3623841;
        double r3623843 = a;
        double r3623844 = m;
        double r3623845 = pow(r3623840, r3623844);
        double r3623846 = r3623843 * r3623845;
        double r3623847 = r3623840 * r3623840;
        double r3623848 = 10.0;
        double r3623849 = r3623840 * r3623848;
        double r3623850 = 1.0;
        double r3623851 = r3623849 + r3623850;
        double r3623852 = r3623847 + r3623851;
        double r3623853 = r3623846 / r3623852;
        double r3623854 = r3623843 / r3623840;
        double r3623855 = r3623850 / r3623840;
        double r3623856 = -r3623844;
        double r3623857 = pow(r3623855, r3623856);
        double r3623858 = r3623857 / r3623840;
        double r3623859 = r3623854 * r3623858;
        double r3623860 = 99.0;
        double r3623861 = r3623860 / r3623847;
        double r3623862 = r3623861 * r3623859;
        double r3623863 = r3623848 * r3623843;
        double r3623864 = r3623857 * r3623863;
        double r3623865 = r3623847 * r3623840;
        double r3623866 = r3623864 / r3623865;
        double r3623867 = r3623862 - r3623866;
        double r3623868 = r3623859 + r3623867;
        double r3623869 = r3623842 ? r3623853 : r3623868;
        return r3623869;
}

Error

Bits error versus a

Bits error versus k

Bits error versus m

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if k < 3.442415825498342e+150

    1. Initial program 0.1

      \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

    if 3.442415825498342e+150 < k

    1. Initial program 10.3

      \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
    2. Using strategy rm

    3. Applied clear-num10.3

      \[\leadsto \color{blue}{\frac{1}{\frac{\left(1 + 10 \cdot k\right) + k \cdot k}{a \cdot {k}^{m}}}}\]

    4. Simplified10.3

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{1 + \left(10 + k\right) \cdot k}{a}}{{k}^{m}}}}\]
    5. Using strategy rm

    6. Applied add-cbrt-cube10.6

      \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{1}{\frac{\frac{1 + \left(10 + k\right) \cdot k}{a}}{{k}^{m}}} \cdot \frac{1}{\frac{\frac{1 + \left(10 + k\right) \cdot k}{a}}{{k}^{m}}}\right) \cdot \frac{1}{\frac{\frac{1 + \left(10 + k\right) \cdot k}{a}}{{k}^{m}}}}}\]

    7. Taylor expanded around inf 10.3

      \[\leadsto \color{blue}{\left(99 \cdot \frac{e^{-1 \cdot \left(\log \left(\frac{1}{k}\right) \cdot m\right)} \cdot a}{{k}^{4}} + \frac{e^{-1 \cdot \left(\log \left(\frac{1}{k}\right) \cdot m\right)} \cdot a}{{k}^{2}}\right) - 10 \cdot \frac{e^{-1 \cdot \left(\log \left(\frac{1}{k}\right) \cdot m\right)} \cdot a}{{k}^{3}}}\]

    8. Simplified0.1

      \[\leadsto \color{blue}{\frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} \cdot \frac{a}{k} + \left(\frac{99}{k \cdot k} \cdot \left(\frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} \cdot \frac{a}{k}\right) - \frac{\left(10 \cdot a\right) \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k \cdot \left(k \cdot k\right)}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 3.442415825498342 \cdot 10^{+150}:\\ \;\;\;\;\frac{a \cdot {k}^{m}}{k \cdot k + \left(k \cdot 10 + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{k} \cdot \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k} + \left(\frac{99}{k \cdot k} \cdot \left(\frac{a}{k} \cdot \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k}\right) - \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)} \cdot \left(10 \cdot a\right)}{\left(k \cdot k\right) \cdot k}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019152 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))